Won't the remaining banks just pass on those extra costs onto the customers anyway? So at the end of the day, "the people" will end up paying for the bail-outs, just with a few extra steps.
Good question. In theory no - it's not supposed to work that way because competition between banks would prevent it. I've no idea how likely it is to happen in practice though. (Edit: But my unqualified guess is that at least some costs will indeed get passed on)